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Statistical Mechanics |
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PHYS 222 |
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Dr.
P. Misra |
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Fall
2002 |
Homework #5 |
Due: 10/11/02 |
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1. |
Assume
that the entropy S and the statistical number W
of a physical system are related through an arbitrary functional form: S = f(W) W represents the total number
of microstates accessible to the system in conformity with a given
macrostate. Show explicitly
that the additive character of S and the multiplicative character of W necessarily require that the function f(W) be of the form : S = kB ln W. |
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2. |
Consider a system of quasi-particles whose energy
eigenvalues are given by e(n) = n h n
; n = 0,1,2 … Obtain an asymptotic expression for the number W of this system, for a given number N of
the quasi-particles and a given total energy E. Determine the temperature T of the system as a function of E/N
and hn, and examine the
situation for which E/(Nhn) >> 1. |
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3. |
Four moles of nitrogen and one mole of oxygen at P
= 1 atm and T = 300K are mixed together to form air at the same pressure and
temperature. Calculate the entropy of
mixing per mole of the air formed. |
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